Problem: Simplify the following expression: $z = \dfrac{-10a^2 + 140a - 450}{a - 9} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-10$ , so we can rewrite the expression: $ z =\dfrac{-10(a^2 - 14a + 45)}{a - 9} $ Then we factor the remaining polynomial: $a^2 {-14}a + {45} $ ${-9} {-5} = {-14}$ ${-9} \times {-5} = {45}$ $ (a {-9}) (a {-5}) $ This gives us a factored expression: $\dfrac{-10(a {-9}) (a {-5})}{a - 9}$ We can divide the numerator and denominator by $(a + 9)$ on condition that $a \neq 9$ Therefore $z = -10(a - 5); a \neq 9$